First, heat 1 tablespoon olive oil in a nonstick sauté pan. Cook the ground beef, breaking it up into small chunks until it is no longer red. Drain the beef on paper towels, then transfer to a heavy-bottomed stock pot.
Next, brown the pork on all sides in the sauté pan and add it to the big pot. Deglaze the sauté pan with a splash of red wine and pour the wine into the pot.
Add 2 tablespoons of olive oil to the sauté pan. When it is medium hot, add 1/2 cup of the onion, all the garlic, 1/2 cup of the celery and 1/2 cup of the bell pepper to the pan and cook until the onion is translucent and limp, about 6 minutes. Add the paprika to the pan; cook, stirring, for 2 minutes. Then add this mixture to the big pot. Deglaze the pan again with another splash of red wine and add the liquid to the big pot.
Add all the remaining ingredients except the mushrooms and salt to the pot. Stir everything together. Bring to a boil, then turn the heat down very low so that everything simmers very slowly. At the start, there should be enough liquid to come up just to the top of the ingredients, not to cover them. (You can add more if you feel nervous—just take that into account at the other end of the process.) Stir occasionally—about every 15 minutes should do it to prevent sticking. After the first two hours, add the mushrooms, and give it all another stir. Keep simmering for at least another hour. I would say four hours is a minimum.
The ragù will be done when the liquid has cooked down so that the sauce is no longer soupy—you want it to be chunky, yet still wet, with the individual pieces clearly visible and everything all melded together into a wonderful fragrant whole.
When the ragù is about ready, cook the pasta according to directions. Drain it well and divide among shallow bowls. Spoon the ragù over the pasta, and serve.